In this paper, an artificial compressibility scheme using the finite element method is introduced. 2002 Zienkiewicz Silver Medal and Prize winning paper. The multi‐purpose CBS scheme is implemented in its fully explicit form to solve incompressible fluid dynamics problems. It is important to note that the scheme developed here includes split and velocity correction. The proposed method takes advantage of good features from both velocity correction and standard artificial compressibility schemes. Unlike many other artificial compressibility schemes, the proposed one works on a variety of grids and gives results for a wide range of Reynold's numbers. The paper presents some bench mark two‐ and three‐dimensional steady and unsteady incompressible flow solutions obtained from the proposed scheme. Copyright © 2003 John Wiley & Sons, Ltd.